https://doi.org/10.26089/NumMet.v27r328

Aspects of solving inverse coefficient problems in medical ultrasound tomography

Authors

  • Alexander V. Goncharsky
  • Ivan I. Makan
  • Dmitry V. Melnik
  • Sergey Y. Romanov
  • Sergey Y. Seryozhnikov

Keywords:

mathematical modeling
ultrasonic 3D tomography
inverse problem
medical imaging
GPU cluster

Abstract

The article is devoted to the development of methods for ultrasonic tomographic imaging of soft tissues in medicine. The main distinction from modern medical devices lies in the use of not only reflected but also transmitted radiation. Mathematical modeling was employed to determine the key parameters of the tomograph. The inverse problem is treated as a coefficient inverse problem for the wave equation, where the unknowns are the speed of sound and attenuation as functions of three spatial coordinates. Efficient numerical methods optimized for the GPU platform have been developed to solve the inverse problem. For experimental verification of the developed technologies, a test bench for ultrasonic tomographic studies has been built, focused on diagnosing breast diseases. Control software for the test bench has been developed, and comprehensive testing of the bench has been carried out. The results of model-based reconstruction of 3D tomographic images are presented.


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Published

2026-07-30

Issue

Vol. 27 (2026): Issue 3.

Section

Methods and algorithms of computational mathematics and their applications

Authors

Alexander V. Goncharsky

Lomonosov Moscow State University, Research Computing Center

• Professor, Head of Laboratory

Ivan I. Makan

Lomonosov Moscow State University, Research Computing Center

• Programmer

Dmitry V. Melnik

Lomonosov Moscow State University, Research Computing Center

• Electronic

Sergey Y. Romanov

Lomonosov Moscow State University, Research Computing Center

• Leading Researcher

Sergey Y. Seryozhnikov

Lomonosov Moscow State University, Research Computing Center

• Engineer

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Copyright (c) 2026 А. В. Гончарский, И. И. Макан, Д. В. Мельник, С. Ю. Романов, С. Ю. Серёжников

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